Deterministic Encryption with the Thorp Shuffle

We analyze the security of the Thorp shuffle, or, equivalently, a maximally unbalanced Feistel network. Roughly said, the Thorp shuffle on N cards mixes any N^1-1/r of them in O(r N) steps. Correspondingly, making O ( r ) passes of maximally unbalanced Feistel over an n -bit string ensures CCA security to 2^n(1-1/r) queries. Our results, which employ Markov chain techniques, particularly couplings, help to justify a practical, although still relatively inefficient, blockcipher-based scheme for deterministically enciphering credit card numbers and the like.